Minnesota Mining and Manufacturing Company (3M), the assignee of this application, has developed a system commercially designated "Finesse-it.TM. System" for removing defects such as dust in paint coatings, and particularly in the new hi-solids enamel coatings used on automobiles, which system is more fully described in advertising brochure No. 60-4400-0344-4 (761)VP available from 3M's Industrial Abrasives Division, the content whereof is incorporated herein by reference. That system includes the use of a cylindrical back up structure with planar end surfaces disposed at angles of about ninety degrees to its axis for supporting pressure sensitive adhesive coated discs of very fine abrasive (e.g., grade 1200 or 1500) during manual manipulation of the back up structure to abrade a defect in a paint coating with the abrasive disc adhered thereto. The end surfaces on the cylindrical back up structure have diameters of about one and one quarter inch or larger which support abrasive discs of slightly larger diameters. Use of the back up structures with such abrasive discs has had a tendency to level surface roughness such as orange peel on portions of the paint surface around the defect being removed, while leveling is undesirably visually detectable if the rest of the paint on the automobile has such surface roughness as is often the case on lower cost automobiles. Also the back up structure is not as convenient to manipulate and store as might be desired.